FTCE Middle Grades Math 5-9 (025) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate grouping symbols first, then exponents and roots, then multiplication and division left to right, and finally addition and subtraction left to right.

Distributive property

For all real numbers a, b, and c, a(b + c) = ab + ac, so a product involving a sum can be rewritten as a sum of products.

Least common multiple

The smallest positive integer divisible by both given numbers; it is found by listing multiples or by multiplying the highest power of each prime factor.

Rational number

Any number expressible as a fraction a/b where a and b are integers and b is not zero; its decimal form either terminates or repeats.

Percent change

The difference between the new and original values divided by the original value, then multiplied by 100 to express the result as a percent.

Scientific notation

A number written as a × 10ⁿ where 1 ≤ |a| < 10 and n is an integer; a positive n indicates a value of at least ten.

Additive inverse

The number that sums with a given number to produce zero; the additive inverse of a is −a, and the additive inverse of −7 is 7.

Slope formula

For two points (x₁, y₁) and (x₂, y₂) with x₁ not equal to x₂, slope m = (y₂ − y₁)/(x₂ − x₁), the vertical change divided by the horizontal change.

Slope-intercept form

The equation y = mx + b, where m is the slope of the line and b is the y-coordinate of the y-intercept, the point (0, b).

Perpendicular line slopes

Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the two slopes equals negative one.

Quadratic formula

For ax² + bx + c = 0 with a not zero, the solutions are x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.

Midpoint formula

The midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2), the average of the corresponding coordinates.

Function

A relation in which each input value is paired with exactly one output value; the vertical line test identifies whether a graph represents one.

Product of powers rule

When multiplying powers that share the same base, add the exponents: aᵐ · aⁿ = aᵐ⁺ⁿ for any real base a and integer exponents m and n.

Pythagorean theorem

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse: a² + b² = c², where c is the hypotenuse.

Triangle angle sum

The three interior angles of any triangle total 180 degrees, and an exterior angle equals the sum of the two remote interior angles.

Circumference of a circle

The distance around a circle, given by C = 2πr or equivalently C = πd, where r is the radius and d is the diameter.

Volume of a cylinder

The space enclosed by a cylinder equals base area times height: V = πr²h, where r is the radius of the circular base and h is the height.

Similar figure scale factor

When two figures are similar with scale factor k, corresponding lengths scale by k, areas scale by k squared, and volumes scale by k cubed.

Polygon interior angle sum

For a polygon with n sides, the interior angles total (n − 2) × 180 degrees; a regular polygon divides that total equally among its angles.

Complement rule

The probability that an event does not occur equals one minus the probability that it does occur: P(not A) = 1 − P(A).

Independent events

Two events are independent when the occurrence of one does not change the probability of the other; in that case P(A and B) = P(A) × P(B).

Interquartile range

The difference between the third quartile and the first quartile, Q3 − Q1; it measures the spread of the middle half of a data set.

Mean versus median

The mean is the sum divided by the count and is pulled toward outliers; the median is the middle ordered value and resists their influence.

Counting principle

If one choice can be made in m ways and a second independent choice in n ways, then the two choices together can occur in m × n ways.

Permutations and combinations

Permutations count ordered arrangements with n!/(n − r)!; combinations count unordered selections with n! divided by r!(n − r)!; order is the distinction.

Formative assessment

Assessment conducted during instruction to reveal current understanding and adjust teaching; examples include exit tickets, questioning, and analysis of student errors.

Summative assessment

Assessment administered after a period of instruction to measure achievement against a standard, such as a unit test or an end-of-course examination.

Concrete to abstract sequence

An instructional progression moving from physical manipulatives to pictorial representations to symbolic notation, supporting student understanding of operations and algebraic ideas.

Bloom's taxonomy

A hierarchy of cognitive objectives ordered as remember, understand, apply, analyze, evaluate, and create, used to classify the demand of tasks and questions.

Depth of knowledge levels

Webb's four levels describe task complexity: recall, application of skills and concepts, strategic thinking, and extended thinking requiring synthesis across contexts.

Validity versus reliability

Validity means an assessment measures the intended construct; reliability means it yields consistent results across repeated administrations, alternate forms, or different scorers.